{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:00.747889Z",
     "start_time": "2025-06-23T10:07:00.734282Z"
    }
   },
   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import torch\n",
    "from d2l import torch as d2l"
   ],
   "outputs": [],
   "execution_count": 24
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:00.795505Z",
     "start_time": "2025-06-23T10:07:00.780388Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def synthetic_data(w, b, num_examples):  #@save\n",
    "    \"\"\"\n",
    "    生成合成数据，数据满足线性关系 y = Xw + b 并添加高斯噪声。\n",
    "\n",
    "    参数:\n",
    "    w (torch.Tensor): 真实的权重向量，是一个一维张量。\n",
    "    b (torch.Tensor): 真实的偏置项，通常是一个标量。\n",
    "    num_examples (int): 要生成的样本数量。\n",
    "\n",
    "    返回:\n",
    "    tuple: 包含两个元素的元组，第一个元素是特征矩阵 X，形状为 (num_examples, len(w))；\n",
    "           第二个元素是标签向量 y，形状为 (num_examples, 1)。\n",
    "    \"\"\"\n",
    "    # 生成服从均值为 0、标准差为 1 的正态分布的随机特征矩阵 X\n",
    "    # 矩阵 X 的形状为 (num_examples, len(w))，其中 num_examples 是样本数量，len(w) 是特征维度\n",
    "    X = torch.normal(0, 1, (num_examples, len(w)))\n",
    "    # 根据线性关系 y = Xw + b 计算标签\n",
    "    # torch.matmul(X, w) 是矩阵乘法，计算 X 与 w 的乘积\n",
    "    y = torch.matmul(X, w) + b\n",
    "    # 为标签 y 添加高斯噪声，噪声服从均值为 0、标准差为 0.01 的正态分布\n",
    "    # 噪声的形状与 y 相同，以确保可以直接相加\n",
    "    y += torch.normal(0, 0.01, y.shape)\n",
    "    # 将标签 y 调整为形状为 (num_examples, 1) 的二维张量\n",
    "    # -1 表示该维度的大小由其他维度自动推断，这里会根据样本数量自动确定\n",
    "    return X, y.reshape((-1, 1))\n",
    "\n",
    "\n",
    "# 定义真实的权重向量，这里有两个特征，所以权重向量是二维的\n",
    "true_w = torch.tensor([2, -3.4])\n",
    "# 定义真实的偏置项\n",
    "true_b = 4.2\n",
    "# 调用 synthetic_data 函数生成 1000 个样本的特征矩阵和标签向量\n",
    "features, labels = synthetic_data(true_w, true_b, 1000)"
   ],
   "id": "54e9dc1a66d74fa1",
   "outputs": [],
   "execution_count": 25
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:00.827092Z",
     "start_time": "2025-06-23T10:07:00.812461Z"
    }
   },
   "cell_type": "code",
   "source": "print('features:', features[0], '\\nlabel:', labels[0])",
   "id": "bd28149ec3d82b5c",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "features: tensor([0.7960, 0.1087]) \n",
      "label: tensor([5.4058])\n"
     ]
    }
   ],
   "execution_count": 26
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:00.983118Z",
     "start_time": "2025-06-23T10:07:00.889468Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 设置图形的大小，使绘制出的图形在视觉上更加合适\n",
    "# d2l.set_figsize() 是 d2l 库中封装好的一个函数，用于设置 matplotlib 图形的大小\n",
    "d2l.set_figsize()\n",
    "\n",
    "# 绘制散点图，用于可视化特征和标签之间的关系\n",
    "# features[:, (1)] 表示从特征矩阵 features 中选取所有行的第 1 列（索引从 0 开始），也就是第二个特征\n",
    "# .detach().numpy() 用于将 PyTorch 张量从计算图中分离出来，并转换为 NumPy 数组，因为 matplotlib 绘图函数通常需要 NumPy 数组作为输入\n",
    "# labels.detach().numpy() 同样是将标签张量从计算图中分离出来并转换为 NumPy 数组\n",
    "# 1 是散点图中每个点的大小，用于控制散点的视觉效果\n",
    "d2l.plt.scatter(features[:, (1)].detach().numpy(), labels.detach().numpy(), 1);\n",
    "\n",
    "'''\n",
    "到此为止，生成了一千个随机数据点\n",
    "'''"
   ],
   "id": "1c2e0c49e07a4020",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\n到此为止，生成了一千个随机数据点\\n'"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 27
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:01.044089Z",
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   "cell_type": "code",
   "source": [
    "def data_iter(batch_size, features, labels):\n",
    "    \"\"\"\n",
    "    该函数用于将特征和标签数据分割成小批量的数据，方便在训练模型时进行批量处理。\n",
    "\n",
    "    参数:\n",
    "    batch_size (int): 每个小批量数据包含的样本数量。\n",
    "    features (torch.Tensor): 特征矩阵，形状为 (样本数量, 特征维度)。\n",
    "    labels (torch.Tensor): 标签向量，形状为 (样本数量,) 或 (样本数量, 1)。\n",
    "\n",
    "    返回:\n",
    "    生成器对象，每次迭代返回一个包含特征和对应标签的小批量数据。\n",
    "    \"\"\"\n",
    "    # 获取特征矩阵中的样本数量\n",
    "    num_examples = len(features)\n",
    "    # 生成从 0 到 num_examples - 1 的整数列表，作为样本的索引\n",
    "    indices = list(range(num_examples))\n",
    "    # 随机打乱样本索引的顺序，确保每次训练时样本的读取顺序是随机的\n",
    "    # 这样可以增加模型训练的随机性，有助于提高模型的泛化能力\n",
    "    random.shuffle(indices)\n",
    "    # 从 0 开始，以 batch_size 为步长遍历样本索引\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        # 截取当前批次的样本索引\n",
    "        # min(i + batch_size, num_examples) 确保在最后一个批次时不会超出样本数量的范围\n",
    "        batch_indices = torch.tensor(\n",
    "            indices[i: min(i + batch_size, num_examples)])\n",
    "        # 通过索引获取当前批次的特征和标签\n",
    "        # 并使用 yield 关键字将它们作为一个元组返回，使函数成为一个生成器\n",
    "        # 生成器在每次迭代时产生一个新的批次，而不是一次性将所有批次都加载到内存中，节省内存资源\n",
    "        yield features[batch_indices], labels[batch_indices]"
   ],
   "id": "69660759bb265e73",
   "outputs": [],
   "execution_count": 28
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:01.090319Z",
     "start_time": "2025-06-23T10:07:01.076273Z"
    }
   },
   "cell_type": "code",
   "source": [
    "batch_size = 10\n",
    "\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print(X, '\\n', y)\n",
    "    break"
   ],
   "id": "73ebc3eb41089435",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-1.3005,  0.3153],\n",
      "        [-1.4897,  0.9817],\n",
      "        [-0.5965, -0.9233],\n",
      "        [-1.5715,  1.4119],\n",
      "        [ 2.1412, -0.1095],\n",
      "        [ 1.0772,  0.7492],\n",
      "        [ 1.0702, -1.0754],\n",
      "        [-0.8299,  0.5699],\n",
      "        [ 0.6444,  0.5310],\n",
      "        [-0.2984, -0.4314]]) \n",
      " tensor([[ 0.5207],\n",
      "        [-2.1254],\n",
      "        [ 6.1524],\n",
      "        [-3.7536],\n",
      "        [ 8.8411],\n",
      "        [ 3.8210],\n",
      "        [10.0064],\n",
      "        [ 0.5986],\n",
      "        [ 3.6909],\n",
      "        [ 5.0859]])\n"
     ]
    }
   ],
   "execution_count": 29
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:01.136259Z",
     "start_time": "2025-06-23T10:07:01.122120Z"
    }
   },
   "cell_type": "code",
   "source": [
    "'''\n",
    "数据批量处理弄好了，开始搞模型参数\n",
    "这里w，b是最开始的随机数字,后面要逐步学习修正的\n",
    "'''\n",
    "w = torch.normal(0, 0.01, size=(2,1), requires_grad=True)\n",
    "b = torch.zeros(1, requires_grad=True)\n",
    "print('w:', w, 'b:', b)"
   ],
   "id": "f95e0932dd74f195",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w: tensor([[ 0.0047],\n",
      "        [-0.0184]], requires_grad=True) b: tensor([0.], requires_grad=True)\n"
     ]
    }
   ],
   "execution_count": 30
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:01.182292Z",
     "start_time": "2025-06-23T10:07:01.167953Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def linreg(X, w, b):  #@save\n",
    "    \"\"\"线性回归模型\"\"\"\n",
    "    return torch.matmul(X, w) + b"
   ],
   "id": "e69f882a786bfbd1",
   "outputs": [],
   "execution_count": 31
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:01.228742Z",
     "start_time": "2025-06-23T10:07:01.213962Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 损失函数\n",
    "def squared_loss(y_hat, y):  #@save\n",
    "    \"\"\"均方损失\"\"\"\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2 #没有求均值"
   ],
   "id": "8744dadddefccc5f",
   "outputs": [],
   "execution_count": 32
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:01.274089Z",
     "start_time": "2025-06-23T10:07:01.260197Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# SGD\n",
    "def sgd(params, lr, batch_size):  #@save\n",
    "    \"\"\"小批量随机梯度下降\"\"\"\n",
    "    with torch.no_grad():\n",
    "        for param in params:\n",
    "            param -= lr * param.grad / batch_size #这里补一下均值\n",
    "            param.grad.zero_() #手动梯度设置0，下一次计算和上一次无关联"
   ],
   "id": "b966c9d66ca4c31d",
   "outputs": [],
   "execution_count": 33
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:01.351778Z",
     "start_time": "2025-06-23T10:07:01.306763Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 定义学习率，学习率控制了每次参数更新的步长大小。\n",
    "# 较大的学习率可能使模型收敛更快，但也可能导致模型无法收敛；较小的学习率则可能使收敛速度变慢，但更稳定。\n",
    "lr = 0.03\n",
    "\n",
    "# 定义训练的轮数，即整个数据集会被模型遍历的次数。\n",
    "# 每一轮中，模型会使用所有的数据进行一次完整的学习和参数更新。\n",
    "num_epochs = 3\n",
    "\n",
    "# 假设 linreg 是一个已经定义好的线性回归模型函数，这里将其赋值给 net。\n",
    "# 这样做的好处是，如果后续要更换模型，只需要修改 net 的赋值即可，提高了代码的可维护性。\n",
    "net = linreg\n",
    "\n",
    "# 假设 squared_loss 是一个已经定义好的均方损失函数，这里将其赋值给 loss。\n",
    "# 均方损失函数用于衡量模型预测值与真实值之间的差异，在训练过程中我们的目标是最小化这个损失。\n",
    "loss = squared_loss\n",
    "\n",
    "# 外层循环控制训练的轮数\n",
    "for epoch in range(num_epochs):\n",
    "    # 内层循环通过 data_iter 函数将数据集分割成小批量数据，每次迭代处理一个小批量\n",
    "    for X, y in data_iter(batch_size, features, labels):\n",
    "        # 计算当前小批量数据的预测值，并通过损失函数计算损失\n",
    "        # net(X, w, b) 是模型根据输入 X、权重 w 和偏置 b 计算得到的预测值\n",
    "        # y 是真实标签，l 是当前小批量数据的损失\n",
    "        l = loss(net(X, w, b), y)\n",
    "\n",
    "        # 因为 l 是一个形状为 (batch_size, 1) 的张量，而不是一个标量。\n",
    "        # 为了计算关于 [w, b] 的梯度，需要将 l 中的所有元素相加得到一个标量\n",
    "        # 然后调用 backward() 方法进行反向传播，计算关于 w 和 b 的梯度\n",
    "        l.sum().backward()\n",
    "\n",
    "        # 调用 sgd 函数（假设已经定义好），使用随机梯度下降算法更新参数 w 和 b\n",
    "        # lr 是学习率，batch_size 用于梯度的归一化\n",
    "        sgd([w, b], lr, batch_size)\n",
    "\n",
    "        # 手动将参数的梯度清零，因为 PyTorch 会累积梯度，为下一次迭代做准备\n",
    "        w.grad.zero_()\n",
    "        b.grad.zero_()\n",
    "\n",
    "    # 使用 torch.no_grad() 上下文管理器，在这个上下文环境中，不进行梯度计算\n",
    "    # 这样可以节省计算资源，因为在验证或测试阶段不需要计算梯度\n",
    "    with torch.no_grad():\n",
    "        # 计算整个训练数据集上的损失\n",
    "        train_l = loss(net(features, w, b), labels)\n",
    "        # 打印当前轮数和对应的训练损失，保留小数点后 6 位\n",
    "        print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')"
   ],
   "id": "8a28de0be79f01b9",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.024771\n",
      "epoch 2, loss 0.000092\n",
      "epoch 3, loss 0.000053\n"
     ]
    }
   ],
   "execution_count": 34
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-23T10:07:03.569256Z",
     "start_time": "2025-06-23T10:07:03.557678Z"
    }
   },
   "cell_type": "code",
   "source": [
    "print(f'w的估计误差: {true_w - w.reshape(true_w.shape)}')\n",
    "print(f'b的估计误差: {true_b - b}')"
   ],
   "id": "1771a12e8299b8e",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w的估计误差: tensor([6.4278e-04, 3.2902e-05], grad_fn=<SubBackward0>)\n",
      "b的估计误差: tensor([0.0015], grad_fn=<RsubBackward1>)\n"
     ]
    }
   ],
   "execution_count": 36
  }
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